Counting BPS States via Holomorphic Anomaly Equations

TL;DR

This paper uses holomorphic anomaly equations to compute Gromov-Witten invariants of a rational elliptic surface, linking them to BPS state counts and affine E8 symmetry, extending BCOV methods.

Contribution

It formulates invariance under affine E8 Weyl group and determines BPS invariants from Gromov-Witten data, connecting to BCOV holomorphic anomaly equations.

Findings

Conjectured BPS state counts from Gromov-Witten invariants.

Established invariance under affine E8 Weyl group.

Connected holomorphic anomaly equations to BCOV framework.

Abstract

We study Gromov-Witten invariants of a rational elliptic surface using holomorphic anomaly equation in [HST1](hep-th/9901151). Formulating invariance under the affine $E_8$ Weyl group symmetry, we determine conjectured invariants, the number of BPS states, from Gromov-Witten invariants. We also connect our holomorphic anomaly equation to that found by Bershadsky,Cecotti,Ooguri and Vafa [BCOV1](hep-th/9302103).